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## How to Calculate Hoop Stress of a Cylinder

**Task:** using Catia V5, compare the hoop stress with the theoretical solution of the cylindrical bar shown below with a clamped end.

**Solution:**

The other end is subjected to a couple caused by opposite forces on a magnitude of 1000 lb separated by 1.5 in. This is equivalent to a torque of 1500 lb applied to the cylinder. The material is steel with Young modulus 30E+6 and a Poisson ratio of 0.3.

The diameter of the cylinder is 1 in. and the dimensions of the loaded end are shown above. Although not shown, the length of the padded cylinder is 5 in. and the length of the padded rectangle is 0.5 in. All sharp corners at the loaded end have a surface fillet radius of 0.1 in.

The strength of materials solution is based on the following, where:

T is the applied torque, r is the radius of the cylinder, and J is the polar moment of inertia.

The hoop stress “C1” which numerically equals τ is calculated.

For the present problem, T = 1400 lb in and D = 1in. Based on these parameters, a value of 7643 psi for the hoop stress is predicted. The FEA results can be assessed by plotting the contour of “C1” at the clamped section. The resulting plot shown below agrees quite well with 7547 psi obtained earlier. The circular fringe patterns are another qualitative check on the validity of the FEA results.